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  <div class="section" id="bootstrapped-dqn">
<h1>Bootstrapped DQN<a class="headerlink" href="#bootstrapped-dqn" title="Permalink to this headline">¶</a></h1>
<p><strong>Actions space:</strong> Discrete</p>
<p><strong>References:</strong> <a class="reference external" href="https://arxiv.org/abs/1602.04621">Deep Exploration via Bootstrapped DQN</a></p>
<div class="section" id="network-structure">
<h2>Network Structure<a class="headerlink" href="#network-structure" title="Permalink to this headline">¶</a></h2>
<img alt="../../../_images/bs_dqn.png" class="align-center" src="../../../_images/bs_dqn.png" />
</div>
<div class="section" id="algorithm-description">
<h2>Algorithm Description<a class="headerlink" href="#algorithm-description" title="Permalink to this headline">¶</a></h2>
<div class="section" id="choosing-an-action">
<h3>Choosing an action<a class="headerlink" href="#choosing-an-action" title="Permalink to this headline">¶</a></h3>
<p>The current states are used as the input to the network. The network contains several $Q$ heads, which  are used
for returning different estimations of the action <span class="math notranslate nohighlight">\(Q\)</span> values. For each episode, the bootstrapped exploration policy
selects a single head to play with during the episode. According to the selected head, only the relevant
output <span class="math notranslate nohighlight">\(Q\)</span> values are used. Using those <span class="math notranslate nohighlight">\(Q\)</span> values, the exploration policy then selects the action for acting.</p>
</div>
<div class="section" id="storing-the-transitions">
<h3>Storing the transitions<a class="headerlink" href="#storing-the-transitions" title="Permalink to this headline">¶</a></h3>
<p>For each transition, a Binomial mask is generated according to a predefined probability, and the number of output heads.
The mask is a binary vector where each element holds a 0 for heads that shouldn’t train on the specific transition,
and 1 for heads that should use the transition for training. The mask is stored as part of the transition info in
the replay buffer.</p>
</div>
<div class="section" id="training-the-network">
<h3>Training the network<a class="headerlink" href="#training-the-network" title="Permalink to this headline">¶</a></h3>
<p>First, sample a batch of transitions from the replay buffer. Run the current states through the network and get the
current <span class="math notranslate nohighlight">\(Q\)</span> value predictions for all the heads and all the actions. For each transition in the batch,
and for each output head, if the transition mask is 1 - change the targets of the played action to <span class="math notranslate nohighlight">\(y_t\)</span>,
according to the standard DQN update rule:</p>
<p><span class="math notranslate nohighlight">\(y_t=r(s_t,a_t )+\gamma\cdot max_a Q(s_{t+1},a)\)</span></p>
<p>Otherwise, leave it intact so that the transition does not affect the learning of this head.
Then, train the online network according to the calculated targets.</p>
<p>As in DQN, once in every few thousand steps, copy the weights from the online network to the target network.</p>
</div>
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